Protecting data confidentiality and integrity paramount in the digital ago. While symmetric encryption algorithms are fast, they struggle with secure key exchange, and asymmetric methods, though secure demand high computational resources. This gap necessitates a balanced cryptographic solution. This research introduces a novel hybrid encryption algorithm that merges the lightweight block-based structure of the SOA algorithm with the strong security features of Elliptic Curve Cryptography (ECC). The proposed method starts by dividing the plaintext into fixed-size blocks, converting characters int ASCII values, and applying alternating arithmetic operations-addition for odd-indexed blocks and subtraction for even-indexed blocks using fixed encryption matrices and a key complexity. In the decryption stage, the process is reversed using the ECC private key, the identity matrix, and a fixed matrix to reconstruct the text. By integrating ECC into the SOA structure, the need for insecure secret key exchange is eliminated, effectively transforming SOA into an asymmetric encryption system. The results demonstrate that the proposed hybrid approach achieves a strong balance between computational efficiency and high security making it suitable for resource constrained environments and secure data transmission........................ Keywords:................ Elliptic Curve Cryptography (ECC), SOA Algorithm, Hybrid Cryptographic Algorithm, Compute initial key, private and public key.